A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like ...
In this paper we consider bounded real-valued functions over the discrete cube, f : {-1, 1}n [-1, 1]. Such functions arise naturally in theoretical computer science, combinatorics...
Irit Dinur, Ehud Friedgut, Guy Kindler, Ryan O'Don...
Abstract. We apply autocorrelation and Walsh coefficients for the investigation of correlation immune and resilient Boolean functions. We prove new lower bound for the absolute ind...
We present a range of new results for testing properties of Boolean functions that are defined in terms of the Fourier spectrum. Broadly speaking, our results show that the propert...
Parikshit Gopalan, Ryan O'Donnell, Rocco A. Served...
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute va...